We define a deterministic metric of “well-behaved data” that enables
searching along the lines of interpolation search. Specifically, define Delta
to be the ratio of distances between the farthest and nearest pair of adjacent
elements. We develop a data structure that stores a dynamic set of n
integers subject to insertions, deletions, and predecessor/successor queries in
O(lg Δ) time per operation. This result generalizes
interpolation search and interpolation search trees smoothly to nonrandom (in
particular, non-independent) input data. In this sense, we capture the amount
of “pseudorandomness” required for effective interpolation search.